A coupled SPH-NSCD DEM model to simulate the interaction between water and solid blocks

This paper presents a fully coupled numerical framework combining the Smoothed Particle Hydrodynamics (SPH) method with a Discrete Element Method (DEM) based on Non-Smooth Contact Dynamics (NSCD) to simulate interactions between free-surface water flows and rigid solid blocks. The SPH method is employed to resolve the Navier-Stokes equations in a fully resolved fluid approach, enabling the simulation of laminar-to-turbulent regimes and complex free-surface phenomena. The motion and contact interactions of rigid bodies are modeled using the NSCD-based DEM, which assumes perfectly rigid bodies and incorporates Signorini's condition and Coulomb friction without regularization. A key feature of the proposed framework is the use of distinct time scales for the fluid and solid phases, allowing the DEM time step to be significantly larger than that of SPH while maintaining numerical stability and accuracy. The coupling strategy ensures consistent transfer of forces and torques between phases through boundary particles attached to rigid bodies. The model is validated against two benchmark experimental configurations: (i) the collapse of submerged cylindrical columns and (ii) three-dimensional dam-break flows impacting rigid cubes. Both qualitative and quantitative comparisons demonstrate that the proposed SPH-NSCD DEM model accurately reproduces the fluid dynamics, block motion, and impact-induced rearrangements. The results highlight the robustness, computational efficiency, and potential of the method for coastal engineering applications involving complex fluid–structure interactions.